Part 14 (1/2)
”Yes, a little What is that? A probleame”
”Impossible!” I exclaimed rather rudely ”The position is a perfect monstrosity!”
He took from his pocket a postcard and handed it to me It bore an address at one side and on the other the words ”43 K to Kt 8”
”It is a correspondence game” he exclai my reply”
”But you really must excuse me; the position seems utterly impossible How on earth, for exaly ”I see; you are a beginner; you play to win”
”Of course you wouldn't play to lose or draw!”
He laughed aloud
”You have much to learn My friend and myself do not play for results of that antiquated kind We seek in chess the wonderful, the whimsical, the weird Did you ever see a position like that?”
I inwardly congratulated myself that I never had
”That position, sir, materializes the sinuous evolvements and syncretic, synthetic, and synchronous concatenations of two cerebral individualities It is the product of an ae of--”
”Have you seen the evening paper, sir?” interrupted the in beside his thu him, I took the paper and read--”Insane, but quite hare”
After that I let the poor fellow run on in his ay until both got out at the next station
But that queer position became fixed indelibly in my mind, with Black's last move 43 K to Kt 8; and a short time afterwards I found it actually possible to arrive at such a position in forty-three moves Can the reader construct such a sequence? How did White get his rooks and king's bishop into their present positions, considering Black can never have iven, and every itimate
MEASURING, WEIGHING, AND PACKING PUZZLES
”Measure still for measure” Measure for Measure, v 1
Apparently the first printed puzzle involving thefrom one vessel to others of known capacity was that propounded by Niccola Fontana, better known as ”Tartaglia” (the sta 24 oz of valuable balsa vessels holding 5, 11, and 13 ounces respectively There are many different solutions to this puzzle in six s from one vessel to another Bachet de Meziriac reprinted this and other of Tartaglia's puzzles in his _Probleeneral opinion that puzzles of this class can only be solved by trial, but I think forenerally of certain related cases It is a practically unexplored field for investigation
The classic weighing problem is, of course, that proposed by Bachet It entails the deterhts that would serve to weigh any integral number of pounds from 1 lb to 40 lbs inclusive, e are allowed to put a weight in either of the two pans The answer is 1, 3, 9, and 27 lbs Tartaglia had previously propounded the sahts may only be placed in one pan The answer in that case is 1, 2, 4, 8, 16, 32 lbs Major MacMahon has solved the probleenerally A full account will be found in Ball's Mathe puzzles, in which we are required to pack a iven dimensions into a box of known dimensions, are, I believe, of quite recent introduction At least I cannot recall any example in the books of the old writers One would rather expect to find in the toy shops the idea presented as a mechanical puzzle, but I do not think I have ever seen such a thing The nearest approach to it would appear to be the puzzles of the jig-saw character, where there is only one depth of the pieces to be adjusted
362--THE WassAIL BOWL
One Christmas Eve three Weary willies came into possession of as to them a veritable wassail bowl, in the for exactly six quarts of fine ale One of the , and the problest them without waste Of course, they are not to use any other vessels or measures If you can shoas to be done at all, then try to find the way that requires the fewest possiblefro as a manipulation
363--THE DOCTOR'S QUERY
”A curious little point occurred to ,” said a doctor ”I had a bottle containing ten ounces of spirits of wine, and another bottle containing ten ounces of water I poured a quarter of an ounce of spirits into the water and shook theether The mixture was then clearly forty to one Then I poured back a quarter-ounce of the ain each contain the same quantity of fluid What proportion of spirits to water did the spirits of wine bottle then contain?”
364--THE BARREL PUZZLE
Theover the liquid contents of a barrel What the particular liquid is it is impossible to say, for we are unable to look into the barrel; so ill call it water One man says that the barrel is more than half full, while the other insists that it is not half full What is their easiest way of settling the point? It is not necessary to use stick, string, or iive this merely as one of the siacity in the solving of puzzles What are apparently very difficult problems may frequently be solved in a similarly easy manner if we only use a little common sense
[Illustration]
365--NEW MEASURING PUZZLE
Here is a new poser inA man has two ten-quart vessels full of wine, and a five-quart and a four-quart measure He wants to put exactly three quarts into each of the two measures How is he to do it? And how s from one vessel to another) do you require? Of course, waste of wine, tilting, and other tricks are not allowed
366--THE HONEST DAIRYMAN
An honest dairy his milk for public consuwater Froh to double the contents of can B Then he poured froh to double its contents Then he finally poured from can A into can B until their contents were exactly equal After these operations he would send the can A to London, and the puzzle is to discover what are the relative proportions of milk and water that he provides for the Londoners' breakfast-tables Do they get equal proportions of milk and water--or two parts ofquestion, though, curiously enough, we are not told how much milk or water he puts into the cans at the start of his operations
367--WINE AND WATER
Mr Goodfellow has adopted a capital idea of late When he gives a little dinner party and the time arrives to smoke, after the departure of the ladies, he sometimes finds that the conversation is apt to become too political, too personal, too slow, or too scandalous Then he always es to introduce to the company some new poser that he has secreted up his sleeve for the occasion This invariably results in no end of interesting discussion and debate, and puts everybody in a good humour
Here is a little puzzle that he propounded the other night, and it is extraordinary how the colass half full of wine, and another glass twice the size one-third full of wine Then he filled up each glass ater and emptied the contents of both into a tumbler ”Now,” he said, ”what part of the ive the correct answer?
368--THE KEG OF WINE
Here is a curious little proble One day he drew off a jugful of wine and filled up the keg ater Later on, when the wine and water had got thoroughlyater It was then found that the keg contained equal proportions of wine and water Can you find fro?
369--MIXING THE TEA
”Mrs Spooner called this rocer to his assistant ”She wants twenty pounds of tea at 2s 4d per lb Of course we have a good 2s 6d tea, a slightly inferior at 2s 3d, and a cheap Indian at 1s 9d, but she is very particular always about her prices”
”What do you propose to do?” asked the innocent assistant
”Do?” exclairocer ”Why, just mix up the three teas in different proportions so that the twenty pounds ork out fairly at the lady's price Only don't put in more of the best tea than you can help, as we make less profit on that, and of course you will use only our co”
Hoas the poor fellow to mix the three teas? Could you have shown him how to do it?
370--A PACKING PUZZLE
As we all know by experience, considerable ingenuity is often required in packing articles into a box if space is not to be unduly wasted A e number of iron balls, all exactly two inches in diameter, and he wished to pack as ular box 24+9/10 inches long, 22+4/5 inches wide, and 14 inches deep Nohat is the greatest number of the balls that he could pack into that box?
371--GOLD PACKING IN RUSSIA
The editor of the Tih Russian official to inspect the gold stored in reserve at St Petersburg, in order that he ht satisfy himself that it was not another ”Humbert safe” He replied that it would be of no use whatever, for although the gold ht appear to be there, he would be quite unable froold A correspondent of the Daily Mail thereupon took up the challenge, but, although he was greatly impressed by what he saw, he was co and counting the contents of every box and sack, and assaying every piece of gold) to give any assurance on the subject In presenting the following little puzzle, I wish it to be also understood that I do not guarantee the real existence of the gold, and the point is not at all old is not usually ”put up” in slabs of the diive, I can only claied in packing 800 gold slabs, each , 11 inches wide, and 1 inch deep What are the interior dith and width, and necessary depth, that will exactly contain the left over? Notto the rules of the govern, and not at all difficult
372--THE BARRELS OF HONEY
[Illustration]
Once upon a tidad as much respected by all who knew him He had three sons, and it was a rule of his life to treat them all exactly alike Whenever one received a present, the other tere each given one of equal value One day this worthyall his possessions to his three sons in equal shares
The only difficulty that arose was over the stock of honey There were exactly twenty-one barrels The old man had left instructions that not only should every son receive an equal quantity of honey, but should receive exactly the same number of barrels, and that no honey should be transferred from barrel to barrel on account of the waste involved Now, as seven of these barrels were full of honey, seven were half-full, and seven were empty, this was found to be quite a puzzle, especially as each brother objected to taking more than four barrels of, the same description--full, half-full, or e a correct division of the property?